Fortunately for them, they no longer need to deal with a brooding running back, a troublesome defensive tackle or a deep threat who frequently drops passes and allegedly punches people and parties too much.
Edwards was jettisoned to the New York Jets Wednesday, giving his new team the apparent big-play receiver it needs. He also gives the Jets an instant distraction who faces an NFL investigation and possible suspension.
When is it worth the risk?
That seems to be one of the most compelling job assignments for any general manager these days, right up there with negotiating contracts and evaluating talent. No need to even ask Jim Hendry about that one.
Arguably, Milton Bradley single-handedly took the Cubs down with his cancerous clubhouse presence and unreliable play. But for much of the season, the question was whether a different Cubs team could absorb Bradley or better yet, make him a better teammate.
For years, it was fair to debate whether Plaxico Burress and Randy Moss, despite their talent, could potentially hurt the Bears more than they could help them. It was believed that only highly successful, veteran-laden teams like the Steelers or Patriots could successfully assimilate either of the two and both did, though the Giants, in particular, certainly had more than their share of trouble with Burress, who is currently serving time for criminal possession of a weapon.
In the case of Moss, the chance to win a Super Bowl apparently was enough to motivate him to improve his behavior.
Many troublemakers have passed through the annals of Chicago sports, perhaps none as successfully as Dennis Rodman, who survived and prospered for several reasons with the Chicago Bulls.
Rodman was a talented player who accepted his role as a rebounder and defender and performed well. He respected Michael Jordan and the Bulls' larger pursuit of greatness too much to sidetrack them. And to that end, Jordan and Phil Jackson also held Rodman accountable. Rodman ventured to the edge of trouble on several occasions but rarely toppled over, and never to the detriment of the team.
Bears players said Wednesday that they could be one of those teams able to absorb a troublemaker like Edwards, which says a lot for how far they've come.
"You've got to trust your locker room," said Adewale Ogunleye, a nine-year NFL veteran who is in his sixth season with the Bears. "If you have a locker room who can bring [a player] in and make him adhere to the culture, you can [do it]. You can't do it on certain teams.
"Everybody here has their own opinions, everybody is free to think the way they want to think and be who they want to be. But at the same time, we have goals we want to accomplish together and we all know that in the back of our minds. That's pretty big here.
"I don't think we'd allow [one guy to disrupt that]. Not as long as Olin [Kreutz] is here. He's as tough as we get."
Sometimes, all kidding aside, all it takes is a leader whom everyone respects, and, said seven-year Bears veteran Jason McKie, a team with chemistry.
"Look at Cincinnati a couple years back," he said. "They had guys getting into trouble all the time but they were a young team. It depends on the type of team you go to. If you got a team that has a lot of older veterans and a solid tradition, they're not going to let somebody come in there and just mess up their chemistry and their tradition of winning.
"We have a lot of guys here who have played with each other for a while and anybody they bring in, they buy into the system as well. You haven't heard of any problems amongst us in here."
McKie said Moss' relatively good behavior with the Patriots after a college career, beginning at Florida State, consumed by controversy, was all about a strong organization refusing to lower its standards.
"Those guys up in New England have been there for a while and they all buy into [Bill] Belichick's system," he said. "You didn't hear about any problems from Randy Moss because when you go there, you know if you want to stay there, you have to buy into the system as well.
"They've been successful for many years just plugging guys in, and a new guy going there knows that even though he's a superstar, they can just release him and plug somebody else in there."
Playing well doesn't hurt.
"That always helps," said tight end Desmond Clark with a smile. "If you're playing and helping the team out, it's a whole lot easier to get along. But when you're losing, other things start to pop up and become more of a point of emphasis."
Odd as it would have sounded a month ago, the Bears don't need Braylon Edwards.
But odder still, they could have survived him.
Melissa Isaacson is a columnist for ESPNChicago.com